Deep Bayesian Filter for Bayes-faithful Data Assimilation

Fuente: arXiv
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Autores principales: Tarumi, Yuta, Fukuda, Keisuke, Maeda, Shin-ichi
Formato: Preprint
Publicado: 2024
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author Tarumi, Yuta
Fukuda, Keisuke
Maeda, Shin-ichi
author_facet Tarumi, Yuta
Fukuda, Keisuke
Maeda, Shin-ichi
contents State estimation for nonlinear state space models (SSMs) is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose Deep Bayesian Filtering (DBF) for data assimilation on nonlinear SSMs. DBF constructs new latent variables $h_t$ in addition to the original physical variables $z_t$ and assimilates observations $o_t$. By (i) constraining the state transition on the new latent space to be linear and (ii) learning a Gaussian inverse observation operator $r(h_t|o_t)$, posteriors remain Gaussian. Notably, the structured design of test distributions enables an analytical formula for the recursive computation, eliminating the accumulation of Monte Carlo sampling errors across time steps. DBF trains the Gaussian inverse observation operators $r(h_t|o_t)$ and other latent SSM parameters (e.g., dynamics matrix) by maximizing the evidence lower bound. Experiments demonstrate that DBF outperforms model-based approaches and latent assimilation methods in tasks where the true posterior distribution on physical space is significantly non-Gaussian.
format Preprint
id arxiv_https___arxiv_org_abs_2405_18674
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Deep Bayesian Filter for Bayes-faithful Data Assimilation
Tarumi, Yuta
Fukuda, Keisuke
Maeda, Shin-ichi
Machine Learning
Atmospheric and Oceanic Physics
Data Analysis, Statistics and Probability
State estimation for nonlinear state space models (SSMs) is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose Deep Bayesian Filtering (DBF) for data assimilation on nonlinear SSMs. DBF constructs new latent variables $h_t$ in addition to the original physical variables $z_t$ and assimilates observations $o_t$. By (i) constraining the state transition on the new latent space to be linear and (ii) learning a Gaussian inverse observation operator $r(h_t|o_t)$, posteriors remain Gaussian. Notably, the structured design of test distributions enables an analytical formula for the recursive computation, eliminating the accumulation of Monte Carlo sampling errors across time steps. DBF trains the Gaussian inverse observation operators $r(h_t|o_t)$ and other latent SSM parameters (e.g., dynamics matrix) by maximizing the evidence lower bound. Experiments demonstrate that DBF outperforms model-based approaches and latent assimilation methods in tasks where the true posterior distribution on physical space is significantly non-Gaussian.
title Deep Bayesian Filter for Bayes-faithful Data Assimilation
topic Machine Learning
Atmospheric and Oceanic Physics
Data Analysis, Statistics and Probability
url https://arxiv.org/abs/2405.18674